Demo: Basics of Percentages, Percentage - Fraction Conversions

Duration: 13 min

This video lesson is available to enrolled students.

Return to /learn/BPSC/part-2-primary-maths/percentage/conversion-between-fractions-ratio-percentages/asset-demo-basics-of-percentages-percentage-fraction-conversions after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | भाषा (हिंदी) / Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, संज्ञानात्मक और रचनावादी अधिगम / Cognitive and Constructivist Learning, वर्णमाला
  3. Section 1 | اردو زبان / Language (Urdu) — 22 Questions (Fixed): رسم الخط، حروفِ تہجی اور املا, اسم، ضمیر اور صفت, الفاظ، محاورے اور ضرب الامثال, تفہیمِ عبارت، انشا اور ترجمہ, تفہیم
  4. Section 1 | বাংলা ভাষা / Language (Bengali) — 22 Questions (Fixed): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি, বাক্য ও বাচ্য, শব্দগঠন ও শব্দভান্ডার, অনুবাদ, বোধপরীক্ষণ ও রচনা
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning / प्राथमिक गणित एवं तर्कशक्ति: Ratio and Proportion / अनुपात और समानुपात, Divisibility Rules / विभाज्यता के नियम, Mixture and Alligation / मिश्रण और एलिगेशन, Permutation and Combination / क्रमचय और संचय, Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, अनुक्रम, श्रेणी और संयोजन / Sequences, Series and Combinatorics, Time, Speed and Distance / समय, चाल और दूरी, Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Non-Verbal Reasoning / अशाब्दिक तर्क, Percentage / प्रतिशत, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Age Problems / आयु संबंधी प्रश्न, Arithmetic / अंकगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Algebra / बीजगणित, Probability / प्रायिकता, Trigonometry / त्रिकोणमिति, Syllogisms / न्यायवाक्य, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी, Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Data Arrangement / आँकड़ों की व्यवस्था, Inequality / असमानता, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Order and Ranking / क्रम एवं रैंकिंग, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  7. Section 2 | General Awareness (GK + Current Affairs) / सामान्य जागरूकता (GK + समसामयिकी): भारतीय संविधान / Indian Constitution, Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, कोशिका: संरचना एवं कार्य / Cell: Structure and Function, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान, ऊष्मागतिकी एवं साम्यावस्था / Thermodynamics and Equilibrium, भारतीय राष्ट्रीय आंदोलन एवं स्वतंत्र भारत / Indian National Movement and Independent India, Geography / भूगोल, भारतीय अर्थव्यवस्था / Indian Economy, Environment / पर्यावरण, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, Trade, Marketing and Consumer Protection / व्यापार, विपणन एवं उपभोक्ता संरक्षण, Cyber Safety and Security, Computer Software, Operating System, Computer Networks, Word Processing (MS Word), Terms & Abbreviations, Presentation Software (MS PowerPoint), Internet of Things, Cloud Computing
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References, OOPS with Java
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video lecture, presented by Yash Jain, provides a comprehensive introduction to the fundamentals of percentages and their conversion into fractions. The lesson begins by establishing the core conceptual understanding of a percentage as a value per hundred, using practical examples like discounts to illustrate how 25% represents Rs. 25 off every Rs. 100 of price. The instructor systematically scales this logic to higher values such as Rs. 200 and Rs. 300, demonstrating proportional calculations for various items including T-shirts and pants. The curriculum then transitions to real-world applications, covering shopping mall discounts, academic marks, population changes, and company performance metrics. A significant portion of the lecture is dedicated to mathematical conversions, specifically teaching how to convert percentages into fractions by dividing by 100 and simplifying the result. This includes handling complex cases involving mixed fractions like 16 + (2/3)% and 83 + (1/3)%. The final segment introduces an important property of percentages, deriving the formula for calculating P% of X as (P/100) * X. The instructor demonstrates this property through step-by-step calculations, such as finding 20% of 800 and comparing A% of B with B% of A, effectively bridging the gap between conceptual understanding and computational application.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with a title slide introducing the topic of Percentages by Yash Jain, setting the stage for the lesson. The instructor immediately moves to basic concepts, posing a critical question: 'What does a discount of 25% mean?' The core definition is established on-screen stating that for every Rs. 100 price, a customer receives a discount of Rs. 25. This foundational concept is reinforced by calculating the net price for a reference value of Rs. 100, showing the subtraction '100 - 25'. The instructor then scales this logic to demonstrate proportional discounts for higher price points, specifically calculating the discount for Rs. 200 as Rs. 50 and for Rs. 300 as Rs. 75, visually displaying the arithmetic '200 - 50' and '300 - 75' to solidify the understanding of percentage as a rate per hundred.

  2. 2:00 – 5:00 02:00-05:00

    Building on the base reference of Rs. 100, the instructor applies the discount concept to a handwritten table listing specific items with varying prices. The visible text shows calculations for a T-shirt priced at 300 (discount 75), Pants at 400 (discount 100), Lower at 200 (discount 50), and Hand gloves at 100 (discount 25). This practical application transitions into a broader discussion on the applications of percentages, with text on screen listing 'Shopping Mall Discounts', 'Marks' (80%, 70%, 60%), and 'Increase or decrease in performance or population'. The instructor demonstrates calculating specific percentage values, such as 30% of 200 resulting in 60 and 30% of 100 resulting in 30. The segment concludes by introducing the rules for converting percentages into fractions, explicitly writing 'Percentage to Fraction (Divide by 100)' and 'Fraction to Percentage (Multiply by 100)' on the board.

  3. 5:00 – 10:00 05:00-10:00

    This segment focuses on the mechanical process of converting percentages to fractions using specific examples. The instructor solves 25% by writing '25/100' and simplifying it to '1/4'. Similarly, 60% is converted to '60/100', simplified to '3/5', and expressed as a ratio '3:5'. The lesson advances to handling mixed fraction percentages, starting with 16 + (2/3)%. The instructor converts the mixed number to an improper fraction '50/3', divides by 100, and simplifies the result to '1/6'. A new example is introduced at the end of this window involving 83 + (1/3)%, where the mixed number is converted to '250/3' before division by 100. The visual evidence shows the step-by-step reduction of these complex fractions, emphasizing the rule to convert mixed numbers to improper fractions first before applying the division by 100 rule.

  4. 10:00 – 12:43 10:00-12:43

    The final section introduces 'An Important Property of Percentages', deriving the general formula for calculating P% of X as (P/100) * X, which simplifies to PX/100. The instructor demonstrates this with a specific calculation of '20% of 800', showing the conversion to '20/100 * 800' and arriving at the result '160'. The lesson concludes by presenting a comparative property on screen: 'A% of B' versus 'B% of A', using the example '75% of 32' and '32% of 75'. The video ends with a closing slide displaying the text 'THANKYOU FOR WATCHING', marking the conclusion of the instructional content on percentage and fraction conversions.

The lecture effectively progresses from conceptual definitions to computational fluency. The teaching strategy relies heavily on the 'per hundred' baseline, using Rs. 100 as a constant reference to explain discounts before scaling to arbitrary numbers like 200 or 300. This scaffolding allows students to grasp the proportional nature of percentages before tackling abstract calculations. The transition from practical applications like shopping discounts and marks to formal mathematical conversions (percent to fraction) is logical, ensuring students understand the utility of percentages in real life before mastering the arithmetic. The handling of mixed fractions like 16 + (2/3)% is a critical technical skill emphasized, requiring the conversion to improper fractions before division. The final property of percentages (A% of B = B% of A) serves as a powerful shortcut for mental math, rounding out the lesson with both fundamental rules and advanced properties. The consistent use of on-screen text to display formulas like 'P/100 * X' and specific calculations ensures that the visual evidence supports the verbal instruction, making it suitable for revision notes.

Loading lesson…